Square Definition and 1000 Threads

Homework Statement In Lee's "Topological Manifolds", there is a result on page 193 called "The Square Lemma" which states that if I denotes the unit interval in \mathbb{R}, X is a topological space, F\colon I\times I\to X is continuous, and f,g,h,k are paths defined by...

Homework Statement what values does the Fourier series for f(t) converge to if t = 0 and t = 2? Homework Equations The Attempt at a Solution My answers the red rectangles for the even function t=0 >> 1 and t=2 -->1.5 and odd function t=0 >> 0 and t=2 -->1.5 because at t=0 is continuity...

Marie on Facebook writes:

Homework Statement A particle of mass m is in the potential V(x) = \left\{ \begin{array}{rl} \infty & \text{if } x < 0\\ -32 \hbar / ma^2 & \text{if } 0 \leq x \leq a \\ 0 & \text{if } x > a. \end{array} \right. (a) How many bound states are there? (b) In the highest energy...

hi... we know the unit of velocity is m/s2 and while calculating the mean square velocity we find the average(or mean) of the 'squares' of the given velocities. then the unit of MEAN SQUARE VELOCITY should be 'm2/s4' then how come its unit is also m/s2 and not m2/s4 ?

Hi, Is is correct to say that the logarithm of base 2 of a number x, is the same thing as the square root of a number x?

ello everybody, how can I calculate the group velocity of a wave package in an infinite square well? I know only how it can be calculated with a free particle, the derivation of the dispersion relation at the expectation value of the moment. But in the well, there are only discrete...

Hi everybody, I’m trying to compute the square root of the following squared block matrix: \begin{equation} M=\begin{bmatrix} A &B\\ C &D\\ \end{bmatrix} \end{equation} (that is M^(1/2))as function of A,B,C, D which are all square matrices. Can you help me? I sincerely...

The part I don't understand is how they show there exists a smaller element. They assume s=t√3 is the smallest element of S={a=b√3: a,b€Z} . Then what they do is add s√3 to both sides and get s√3-s=s√3-t√3. I don't get how they thought of that or why it works.I know there exists an element...

Let f(x) = ax - \dfrac{x^3}{1+x^2} where a is a constant Show that, if a ≥ 9/8 then f'(x) ≥ 0 first problem when taking the derivative in the solution they seem to have jumped a step which I don't see how: f'(x) = a - \dfrac{3x^2(1+x^2) - 2x(x^3)}{(1+x^2)^2} = \dfrac{a + (2a - 3)x^2 + (a...

Homework Statement Finding derivative of (sin(sqt3x+5)) Homework Equations None given. Chain Rule The Attempt at a Solution The answer is: (cos(sqrt3x+5)) * 1/2(sqrt3x+5) * 3 but I don't know how to get to the 3. I turned sin into cos and multiplied by the inside derivative giving the...

Prove that $$\int_0^{\pi/2} (\log \sin x )^2 dx = \frac{1}{24} \left(\pi ^3+12 \pi \log^2(2)\right)$$

k is a square modulo m?? \:Homework Statement This is a portion of the problem. I have to prove that A holds if and only if k is a square modulo m. I have no idea what "k is a square modulo m" means. Homework Equations The Attempt at a Solution I've looked it up online and found some PDF's...

Homework Statement Homework Equations The Attempt at a Solution Alright so the solution is in the above pic, but I can't get anywhere close. You can see from the green circles that the "squares" aren't matching up. So I'm not sure if I can't multiply fractions anymore or what.

dear users I have a problem in finding eigenvalues of a 12*12 because the 12*12 matrix is so complicated so i decided to first make my 12*12 matrix in form of upper triangular form but I don't know how can I do it with MATLAB or mathematica? can you please tell me that what is the formula in...

If I have a periodic function that is say a sum of a number of sine functions I can use a Fourier Transform to get the component functions. Now, if I have a bunch of square waves of differing amplitudes and frequencies that I add up into a resultant waveform. Given that waveform what'd be...

Why n*p always equal to ni square?? (semiconductor) Hi, For you guys who studied semiconductor physics must be familiar with the equation: np=ni2 I can understand why this is true for the intrinsic case (the broken bonds would always provide electron and hole in pairs ) But why is this...

Homework Statement Two tiny objects with equal charges of 6.00uC are placed at the two lower corners of a square with sides of 0.580m. When facing the square, Point A is the top left corner. Point B is in the top middle. Point C is dead center inside the square. Find the electric...

My book is showing this as an intuitive step, but I'm not quite seeing the reasoning behind it. n**(c/n) → 1 as n → ∞, for, I think, any positive c. But why?

Homework Statement Suppose an ideal bose gas sees a periodic potential with a period a in both x and y directions. Its eigenstates are altered from the free-particle form. The lowest band has energies \epsilon_\vec{k}=2t(2-cos(k_xa)-cos(k_ya)) where t is an energy scale that depends on the...

Homework Statement m and n are positive integers with m,n≥2 where m^2=kn^2 The Attempt at a Solution we know that all prime factors of m have an even amount , their are no prime factors that are repeated an odd number of times. The same goes for n. if k is not a perfect square...

Hi, using a PIC12F683 I'm attempting to toggle an IO pin every time the internal timer overflows (via the timer interrupt) but I can't seem to get it working. I'm viewing the voltage of the pin on a scope, expecting a square wave and getting a constant 5 volts. Also I've read the official...

Is there any algorithm to form a magic square of any size with a desired magic sum ? Also can we make a magic square not only with the numbers from 1 to n2 but using any random numbers ?

Homework Statement Let e be the number close to sqrt(a) by Newtons Method (That is picking a number, diving a by it, and taking their average, divide a by average, get a number, find their average, so on). Using |e<sqrt(a)+e| prove that if |a/e-e|<1/10 then |sqrt(a)-e|<1/10 Note that e is...

Please I'm new here, and would need your help with identifying what sort of potential function is described by the following expression: V(x) = 0 for |x| < 1, =1 at x = \pm 1, and =\infty for |x|>1. (Note that: \pm is plus (+) or minus (-) sign). Could it be referred to as the infinite...

Ok...this must sound stupid, because i didn't found answer on the web and on my books...but i am having trouble with the infinite square well. I want to calculate <x>. V(x)=0 for 0<=x<=a <x>=\frac{2}{a}\int^{a}_{0} x \sin^2(\frac{n\pi}{a}x)dx Doing integration by parts i got to...

Hi, I have a quick question about making quantum mechanics relativistic by simply replacing the hamiltonian by a relativistic hamiltonian. If we write the hamiltonian operator as: H = \sqrt{P2c2 + m2c4}, schrodinger's equation in position basis becomes: i\hbar\dot{\psi} =...

Homework Statement Here's an image http://i.imgur.com/oC8Y6.jpg Homework Equations The wave function for an infinite square well, the expectation values and operators for momentum and I guess the normalization condition? I don't really know because I don't understand the question. The...

The length of the side of the square is a. The boundary conditions are the following: (1) the left edge is kept at temperature T=C2 (2) the bottom edge is kept at temperature T=C1 (3) the top and right edges are perfectly insulated, that is \dfrac{\partial T}{\partial x}=0,\dfrac{\partial...

Homework Statement There was a question on my exam a few days ago. Using Lagrange to find the max/min on a region. We only had to answer a certain amount of questions and I never got to this one. I'm working on it now though out of curiosity. R = { (x,y) | x2 + xy + y2 ≤ 3 } f(x,y) =...

Homework Statement A particle in an infinite box is in the first excited state (n=2). Obtain the expectation value 1/2<xp+px> 2. The attempt at a solution Honestly, I don't even know where to begin. I assumed V<0, V>L is V=∞ and 0<V<L is V=0 I tried setting up the expectation...

Hi guys, attached is a picture of my problem and it is also underlined. I've been reading through this theory and I just don't understand what the square brackets indicate. I understand that ∇phi is the partial derivative with respect to the scalar function phi. But what is ∇phi...

Hi I'm a high school student and need help with the calculations for a bike design. I am required for the design to use 1.5" mild steel square tubing at 1/16" thick for it. I need to know what the strength of the tubing is before i can make or tweak the design. Can anyone help with my predicament?

Homework Statement Please evaluate the line integral \oint dr\cdot\vec{v}, where \vec{v} = (y, 0, 0) along the curve C that is a square in the xy-plane of side length a center at \vec{r} = 0 a) by direct integration b) by Stokes' theoremHomework Equations Stokes' theorem: \oint V \cdot dr =...

If I have a matrix valued function A(x) of some scalar x, how do I compute the derivative of the square root of A with respect to x? It seems like it should be simple, but I can't find it anywhere on the internet. Thanks!

A is not square but rank(A) = rank(A') ? Hi Can anyone help with understand a basic idea, I have a matrix A in MATLAB which is 100x3000. I have checked and there exist many columns of A that are all zeros. But apparently rank(A) = rank(A') = 100 Wikipedia states that the rank of an m x n...

Is the answer to sqrt -81y^3 : y sqrt-81y? or is there no real solutions? Also for this radical equation: sqrt 2n-5 - sqrt 3n+4=2 I worked it out and can't seem to get an answer. Is there no real solutions?

Homework Statement Homework Equations My question too :) The Attempt at a Solution Can anybody confirm whether I solved the problem right or wrong? As for the next question about verilog and many clocks I am unable to find a source with that information. Thanks a lot for any...

Homework Statement Please see the attached. It is a badly drawn sphere :-p By common sense,the area of the shaded region in the sphere = area of square = r^2 But can anyone show me the mathematical proof? Moreover,does it apply to the reality? Imagine when you bend a square sheet with...

At first I thought that there is no square matrix whose square is the 0 matrix. But I found a counterexample to this. My counterexample is: \left( \begin{array}{cc} 0 & 0 \\ 0 & 1 \end{array} \right) However it appears that my counterexample has a 0 row. I'm curious, must a square root of...

Homework Statement a) Explain how any square matrix A can be written as A = QS where Q is orthogonal and S is symmetric positive semidefinite. b) Is it possible to write A = S_1 Q_1 Where Q1 is orthogonal and S1 is symmetric positive definite? Homework Equations A = U \Sigma...

Homework Statement On a 8x8 chess board format an Integer program to optimize the amount of knights required such that every square is covered by at least one knight. Homework Equations I know of a similar problem where we use duality for the placing 5 queens such that the maximum...

a function for a line in a square (or a triangle or a pentagon etc) I don't have one off the top of my head (my maths is very rusty) but I think that ,starting from a cartesian point it is possible to create a function that allows one to draw a polygon in 2 or 3(?) dimensions. This...

Homework Statement If M is a square matrix, prove: (A, MB) = (adj(M)A, B) where (A, MB) denotes the scalar product of the matrices and adj() is the adjoint (hermitian adjoint, transpose of complex conjugate, M-dagger, whatever you want to call it!) Homework Equations adj(M)=M(transpose of...

Hi I often see the following in books but I do not understand how they are equal. So can someone please tell me for what conditions does the following equality hold? (\frac{dy}{dx}) 2 = (d2 y)/(dx2)

Homework Statement Ok, working on a inverse function question, and I got stuck with something. Can someone explain the steps that makes this possible here. Something I am missing :( f(x) = √(x^3 + x^2 + x + 1) How is the inverse of the above function this... 3x^2 + 2x + 1 / 2√(x^3 + x^2 +...

Hi, I am new to Math so I am trying to get some intuition. Let's say I have a matrix A of n x n and a vector B of n x 1 what is the difference between A x B and A' x B? Thanks

Hi I have attached my attempt of solving the infinite square well for Energy. The value I get is different from that of the book, also in the attachment, Kindly explain if my answer is correct given the fact that I proceeded step by step and used no tricks. Thank you.

Homework Statement Let A and B be two square matrices of order n such that AB = A and BA = B. Then, what is the value of [(A + B)t]2? Homework Equations The Attempt at a Solution [(A + B)t]2 = AtAt + AtBt + BtAt + BtBt. I tried to use the fact that AB = A and BA = B to keep...